Notes for Adding/Subtracting Square Roots with like radicals
What would your solution be if you added 2 rational numbers together?
Rational number,
Irrational number,
neither
What would your solution be if you added 1 rational number and 1 irrational
number together?
Rational number,
Irrational number,
neither
What would your solution be if you added 2 irrational numbers together?
Rational number,
Irrational number,
neither
Steps
Are they like radicals?
If they are just add or subtract the
outside numbers.
Work
𝟐√𝟓 + 𝟒√𝟓
Leave the radicands the same.
Steps
Are they like radicals?
If they are just add or subtract the
outside numbers.
Work
𝟏𝟐√𝟕 − 𝟒√𝟕
Leave the radicands the same.
Steps
Are they like radicals?
If they are just add or subtract the
outside numbers.
Work
√𝟑 + √𝟑
Leave the radicands the same.
Steps
Are they like radicals?
If they are just add or subtract the
outside numbers.
Leave the radicands the same.
Work
√𝟓 − 𝟑√𝟓
Notes for Adding/Subtracting Square Roots with unlike radicals
Steps
Are the radicals the same?
Look for a perfect square for each radical
that you can factor out of radicand.
Work
√𝟏𝟐 + √𝟕𝟓
Take the square root of any perfect
square that is a factor.
Leave all remaining numbers under the
radical.
Now are there like radicals? If so add or
subtract the outside numbers if not leave
as is.
Steps
Are the radicals the same?
Look for a perfect square for each radical
that you can factor out of radicand.
Take the square root of any perfect
square that is a factor.
Leave all remaining numbers under the
radical.
Now are there like radicals? If so add or
subtract the outside numbers if not leave
as is.
Work
√𝟑𝟐 + √𝟓𝟎
Steps
Are the radicals the same?
Look for a perfect square for each radical
that you can factor out of radicand.
Work
𝟒√𝟓 + 𝟔√𝟐𝟎
Take the square root of any perfect
square that is a factor.
Leave all remaining numbers under the
radical.
Now are there like radicals? If so add or
subtract the outside numbers if not leave
as is.
Steps
Are the radicals the same?
Look for a perfect square for each radical
that you can factor out of radicand.
Take the square root of any perfect
square that is a factor.
Leave all remaining numbers under the
radical.
Now are there like radicals? If so add or
subtract the outside numbers if not leave
as is.
Work
√𝟕𝟐 + √𝟓𝟎